Abstract:By using Geogebra in the following manuscript, an analysis of the Goldbach conjecture is made. It has been verified through algebraic expressions that there is always a minimum amount of prime elements that make the conjecture for any natural pair number . The graph that is generated by the Graphical Method of the Goldbach Conjecture is taken into consideration, in which the variables that intervene in the axis of the ordinates and the abscissas are examined. After this, certain known even numbers were studied which the number of existing prime numbers is known. Later, it is separated from any number in intervals from 1 to and from N to , thus, finding the prime numbers in the first one. The aforementioned interval is greater than the number of prime elements of the second, with these results and the analysis made to the graph of the aforementioned Graphic Method, it is concluded that the distribution of the primes is related to the natural logarithm function; as it is expressed in the Theorem of the Prime Numbers, but in this case with a slight variant for each of the aforementioned intervals. A probability analysis to verify that the number of intersections that occur is intrinsically related to the function that limits the number of prime elements was performed. This is also related to the function proposed by Gauss.